Question: Solve for $x$ and $y$ using elimination. ${-3x+4y = 5}$ ${-4x-y = -44}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $4$ ${-3x+4y = 5}$ $-16x-4y = -176$ Add the top and bottom equations together. $-19x = -171$ $\dfrac{-19x}{{-19}} = \dfrac{-171}{{-19}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-3x+4y = 5}\thinspace$ to find $y$ ${-3}{(9)}{ + 4y = 5}$ $-27+4y = 5$ $-27{+27} + 4y = 5{+27}$ $4y = 32$ $\dfrac{4y}{{4}} = \dfrac{32}{{4}}$ ${y = 8}$ You can also plug ${x = 9}$ into $\thinspace {-4x-y = -44}\thinspace$ and get the same answer for $y$ : ${-4}{(9)}{ - y = -44}$ ${y = 8}$